Compound Interest

[KWF]

How do I convert P(1 + r)[sup:1epopxpk]3[/sup:1epopxpk] and P( 1 + r)[sup:1epopxpk]4[/sup:1epopxpk], etc. to the expanded form?
I get confused by the factored version P(1 + r)[sup:1epopxpk]n[/sup:1epopxpk]. This does not help me to understand.

For example, P(1 + r)[sup:1epopxpk]2[/sup:1epopxpk] equals (P + rP) + r(P + rP). Show how this occurs with three and four years.

I thank you for your reply.

 

[Deleted member 4993]

How do I convert P(1 + r)[sup:1pc6yh7p]3[/sup:1pc6yh7p] and P( 1 + r)[sup:1pc6yh7p]4[/sup:1pc6yh7p], etc. to the expanded form?
I get confused by the factored version P(1 + r)[sup:1pc6yh7p]n[/sup:1pc6yh7p]. This does not help me to understand.

For example, P(1 + r)[sup:1pc6yh7p]2[/sup:1pc6yh7p] equals (P + rP) + r(P + rP). Show how this occurs with three and four years.

I thank you for your reply.

This was answered in:

viewtopic.php?f=17&t=39976&p=155126#p155126

Did you get pencil/paper and work it out?

 

[KWF]

No, I did not!

It is difficult to "work things out" if one doesn't understand what there is to "work out"!
I haven't had algebra in years!

 

[Denis]

I don't think you realise how silly what you're asking is...but here tizz:

P(1 + r)^3 = (P + rP) + r(P + rP) + r((P + rP) + r(P + rP))

P(1 + r)^4 = (P + rP) + r(P + rP) + r((P + rP) + r(P + rP)) + r((P + rP) + r(P + rP) + r((P + rP) + r(P + rP))

You can make this less silly/wieldy by letting x = P + rp :
P(1 + r)^4 = x + rx + r(x + rx) + r[r + rx + r(x + rx)]

While at it, let y = x + rx:
P(1 + r)^4 = y + ry + r(y + ry)